We study hybrid systems from a global geometric perspective as piecewise smooth dynamical systems. Based on an earlier work, we define the notion of the hybrifold as a single piece-wise smooth state space reflecting the dynamics of the original system. Structural stability for hybrid systems is introduced and analyzed in this framework. In particular, it is shown that a Zeno state is locally structurally stable and that a standard equilibrium on the boundary of a domain implies structural instability.
QC 20160316